where \(f\left( D,\beta \right) , \beta >0\), is an elliptic pseudo-differential operator. We also show that the fundamental solution is the transition density of a Markov process with state space \(\mathbb{Q}_p^n \).

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Ismagilov, R.S.: On the spectrum of the self-adjoint operator in L2(K) where K is a local field; an analog of the Feynman–Kac formula. Theor. Math. Phys. 89, 1024–1028 (1991)CrossRefMathSciNetGoogle Scholar